1. A section-based queueing-theoretical traffic model for congestion and travel time analysis in networks
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2. Agenda Title translation and model introduction Motivating question
Assumptions
Key steps
Results
Questions
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3. Title translation and model introduction
Separated by capacity:
A section-based …
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4. Title translation and model introduction
Separated by capacity:
Highway with multiple lines
A section-based …
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5. Title translation and model introduction
Separated by capacity:
Highway with multiple lines
Off-ramp, single line
A section-based …
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6. Title translation and model introduction
Separated by capacity:
Highway with multiple lines
Off-ramp, single line
Main street, multiple lines
A section-based …
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7. Title translation and model introduction
Points of interest:
A section-based …
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8. Title translation and model introduction
Points of interest:
Measure the flow
A section-based …
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9. Title translation and model introduction
Points of interest:
Measure the flow
Reasons for capacity change:
A section-based …
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10. Title translation and model introduction
Points of interest:
Measure the flow
Reasons for capacity change:
On- or off-ramp
A section-based …
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11. Title translation and model introduction
Points of interest:
Measure the flow
Reasons for capacity change:
On- or off-ramp
Change in number of lines
A section-based …
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12. Title translation and model introduction
Points of interest:
Measure the flow
Reasons for capacity change:
On- or off-ramp
Change in number of lines
Change of gradient
A section-based …
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13. Title translation and model introduction
queueing-theoretical …
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14. Title translation and model introduction
traffic model for congestion …
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15. Title translation and model introduction
and travel time analysis in networks
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16. Title translation and model introduction
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17. Title translation and model introduction
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18. Agenda Title translation and model introduction  Motivating question
Assumptions
Key steps
Results
Questions
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19. Motivating question
What is the expected travel time for a traffic member to go from A to B?
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20. Motivating question
What is the expected travel time for a traffic member to go from A to B, passing a certain network, including dynamic vehicle density?
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21. Agenda Title translation and model introduction 
Motivating question 
Assumptions
Key steps
Results
Questions
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22. Assumption 1
Below some critical vehicle density , the relation between the traffic flow and density is linear
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23. Assumption 2
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24. Assumption 2 Propagation speed of density variation in
free traffic: the average speed of the cars (30 km/h)
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25. Assumption 2 Propagation speed of density variation in
free traffic: the average speed of the cars (30 km/h)
congested traffic: Shockwave formulas => … => 20 km/h
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26. Assumption 3
The length of the congested area is given by integrating over
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27. Assumption 3
The length of the congested area is given by integrating over
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28. Assumption 3
The length of the congested area is given by integrating over
In english:
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29. Assumption 4 The capacity of a congested road = outflow - bottleneck
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30. Assumption 4 The capacity of a congested road = outflow - bottleneck
Less cars can leave the section, but the arrival rate stays the same
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31. Assumption 4 The capacity of a congested road = outflow - bottleneck
Less cars can leave the section, but the arrival rate stays the same
Congestion grows
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32. Assumption 4 The capacity of a congested road = outflow - bottleneck
Less cars can leave the section, but the arrival rate stays the same
Congestion grows
More cars can leave the section, arrival rate stays the same
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33. Assumption 4 The capacity of a congested road = outflow - bottleneck
Less cars can leave the section, but the arrival rate stays the same
Congestion grows
More cars can leave the section, arrival rate stays the same
Congestion gets reduced
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34. Agenda Title translation and model introduction 
Motivating question 
Assumptions 
Key steps
Results
Questions
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35. Key steps
We saw:
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36. Key steps
We saw:
Choice of parameters
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37. Key steps We saw: Choice of parameters Definition of the model
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38. Key steps We saw: Choice of parameters Definition of the model
Choice of assumptions
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39. Key steps Next step: Introduction of road states: Sandro Huber

40. Key steps Next step: Introduction of road states: 0: Free traffic
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41. Key steps Next step: Introduction of road states: 0: Free traffic
1: Completely congested road
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42. Key steps Next step: Introduction of road states: 0: Free traffic
1: Completely congested road
2: Partially congested road
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43. Key steps Final step: Definition of the departure rate Sandro Huber

44. Key steps
Case: Free traffic here and no congestion in the next section
Cars drive through:
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45. Key steps
Case: Partial or complete congestion here, no in next section
Fight through local jam: Assumption 4 =>
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46. Key steps Case: Next section is completely congested
Its totally dependent on how the traffic rolls in the next section:
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47. Agenda Title translation and model introduction 
Motivating question 
Assumptions 
Key steps 
Results
Questions
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48. Results
We now can derive a general relationship for the average travel time trough a section:
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49. Results
We now can derive a general relationship for the average travel time trough a section:
When we enter the section i at time t, we will leave this section when the vehicles that are in section i at time t have passed throught it. We can derivate the following formula:
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50. Results
We now can derive a general relationship for the average travel time trough a section:
When we enter the section i at time t, we will leave this section when the vehicles that are in section i at time t have passed throught it. We can derivate the following formula:
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51. Results
We now can derive a general relationship for the average travel time trough a section:
When we enter the section i at time t, we will leave this section when the vehicles that are in section i at time t have passed throught it. We can derivate the following formula:
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52. Results
Making use of some maths reveals
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53. Results Making use of some maths reveals
So, what does this formula mean?
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54. Results Making use of some maths reveals
So, what does this formula mean?
The travel time increases with time, when the arrival rate at time exceeds the departure time at time (when I want to leave)
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55. Results Making use of some maths reveals
So, what does this formula mean?
The travel time increases with time, when the arrival rate at time exceeds the departure time at time (when I want to leave)
Else, the congestion shrinks, the travel time decreases
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56. Results Making use of some maths reveals
So, what does this formula mean?
The travel time increases with time, when the arrival rate at time exceeds the departure time at time (when I want to leave)
Else, the congestion shrinks, the travel time decreases
Fascinating detail: no velocities in the formula!
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57. Results
Example: Assume you enter the double-lined highway. The arrival rate at 9:30 am is 50 cars/minute. 15 minutes later you arrive at the off-ramp, but just in front of it happened an accident. The police closed one line. Due to this bottleneck the departure rate drops from 50 to 10.
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58. Results
Example: Assume you enter the double-lined highway. The arrival rate at 9:30 am is 50 cars/minute. 15 minutes later you arrive at the off-ramp, but just in front of it happened an accident. The police closed one line. Due to this bottleneck the departure rate drops from 50 to 10. Apply the formula:
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59. Results
Example: Assume you enter the double-lined highway. The arrival rate at 9:30 am is 50 cars/minute. 15 minutes later you arrive at the off-ramp, but just in front of it happened an accident. The police closed one line. Due to this bottleneck the departure rate drops from 50 to 10. Apply the formula: Because 4 > 0, the average travel time grows
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60. Results
So, we did:
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61. Results
So, we did:
Some fancy modelling
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62. Results So, we did: Some fancy modelling Some fancy math Sandro Huber

63. Results We did: Some fancy modelling… Some fancy math…
Some fancy deductions…
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64. Results
What fancy stuff can we do with this?
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65. Results What fancy stuff can we do with this?
Predict the average travel time for a single vehicle
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66. Results What fancy stuff can we do with this?
Predict the average travel time for a single vehicle
Predict time loss due to a building site
Is a detour needed?
Is it even feasible?
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67. Results What fancy stuff can we do with this?
Predict the average travel time for a single vehicle
Predict time loss due to a building site
Is a detour needed?
Is it even feasible?
Model real traffic situations/systems and simulate solutions/changes on computers
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68. Results What fancy stuff can we do with this?
Predict the average travel time for a single vehicle
Predict time loss due to a building site
Is a detour needed?
Is it even feasible?
Model real traffic situations/systems and simulate solutions/changes on computers
Ect…
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69. Agenda Title translation and model introduction 
Motivating question 
Assumptions 
Key steps 
Results 
Questions
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70. Thanks for your attention!
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71. Questions
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